Computing the $L_1$ Geodesic Diameter and Center of a Simple Polygon in Linear Time
Computational Geometry
2015-01-13 v2
Abstract
In this paper, we show that the geodesic diameter and center of a simple polygon can be computed in linear time. For the purpose, we focus on revealing basic geometric properties of the geodesic balls, that is, the metric balls with respect to the geodesic distance. More specifically, in this paper we show that any family of geodesic balls in any simple polygon has Helly number two, and the geodesic center consists of midpoints of shortest paths between diametral pairs. These properties are crucial for our linear-time algorithms, and do not hold for the Euclidean case.
Keywords
Cite
@article{arxiv.1312.3711,
title = {Computing the $L_1$ Geodesic Diameter and Center of a Simple Polygon in Linear Time},
author = {Sang Won Bae and Matias Korman and Yoshio Okamoto and Haitao Wang},
journal= {arXiv preprint arXiv:1312.3711},
year = {2015}
}
Comments
10-page Abstract appeared in the proceedings of LATIN 2014